A qubit strongly interacting with a bosonic environment: Geometry of thermal states

TL;DR

This paper investigates the nature of thermal states in a strongly coupled qubit-bosonic environment, proposing that such states are diagonal in the pointer basis rather than the energy eigenbasis, challenging traditional thermodynamics.

Contribution

It introduces a model showing that strong system-environment interactions lead to thermal states aligned with the pointer basis, not the energy basis, as traditionally assumed.

Findings

Thermal states in strong coupling are diagonal in the pointer basis.

The model demonstrates the projection of Gibbs states onto pointer states.

Strong coupling alters the basis in which decoherence occurs.

Abstract

A standard theory of thermodynamics states that a quantum system in contact with a thermal environment relaxes to the equilibrium state known as the Gibbs state wherein decoherence occurs in the system's energy eigenbasis. When the interaction between the system and environment is strong, a different equilibrium state can be reached that is not diagonal in the system energy eigenbasis. Zurek's theory of einselection predicts that the decoherence takes place in the so-called pointer basis under the strong coupling regime, which can be viewed as continuous measurement of the system by the environment. The thermal state under the strong coupling regime is thus expected to be diagonal in the pointer states rather than energy eigenstates. We have postulated that the thermals state in the strong coupling limit is a Gibbs state projected onto the pointer basis and have demonstrated this with a simple model of single qubit strongly interacting with a bosonic environment.